An introduction to the Ginzburg-Landau theory of phase transitions and nonequilibrium patterns

Understand

This paper presents an introduction to phase transitions and critical phenomena on the one hand, and nonequilibrium patterns on the other, using the Ginzburg-Landau theory as a unified language.

• In the first part, mean-field theory is presented, for both statics and dynamics, and its validity tested self-consistently.
• As is well known, the mean-field approximation breaks down below four spatial dimensions, where it can be replaced by a scaling phenomenology.
• The Ginzburg-Landau formalism can then be used to justify the phenomenological theory using the renormalization group, which elucidates the physical and mathematical mechanism for universality.